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Recent questions and answers in Numerical Methods
1
vote
1
answer
1
GATE CSE 1987 | Question: 1-xxiv
The simplex method is so named because It is simple. It is based on the theory of algebraic complexes. The simple pendulum works on this method. No one thought of a better name.
Arjun
answered
in
Numerical Methods
May 26, 2022
by
Arjun
534
views
gate1987
numerical-methods
simplex-method
out-of-gate-syllabus
0
votes
1
answer
2
NIELIT 2016 MAR Scientist B - Section B: 7
In which of the following methods proper choice of initial value is very important? Bisection method False position Newton-Raphson Bairsto method
33
answered
in
Numerical Methods
Mar 16, 2022
by
33
1.4k
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nielit2016mar-scientistb
non-gate
numerical-methods
8
votes
3
answers
3
GATE IT 2006 | Question: 28
The following definite integral evaluates to $\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$ $\frac{1}{2}$ $\pi \sqrt{10}$ $\sqrt{10}$ $\pi$
ankitgupta.1729
answered
in
Numerical Methods
Sep 14, 2021
by
ankitgupta.1729
3.6k
views
gateit-2006
numerical-methods
normal
non-gate
1
vote
3
answers
4
GATE CSE 2008 | Question: 21
The minimum number of equal length subintervals needed to approximate $\int_1^2 xe^x\,dx$ to an accuracy of at least $\frac{1}{3}\times10^{-6}$ using the trapezoidal rule is 1000e 1000 100e 100
omji-mishra
answered
in
Numerical Methods
Aug 3, 2021
by
omji-mishra
2.3k
views
gatecse-2008
normal
numerical-methods
trapezoidal-rule
non-gate
2
votes
1
answer
5
GATE CSE 1988 | Question: 1i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
Jhaiyam
answered
in
Numerical Methods
Aug 1, 2020
by
Jhaiyam
379
views
gate1988
numerical-methods
out-of-gate-syllabus
2
votes
2
answers
6
UGC NET CSE | June 2019 | Part 2 | Question: 10
Consider an LPP given as $\text{Max } Z=2x_1-x_2+2x_3$ subject to the constraints $2x_1+x_2 \leq 10 \\ x_1+2x_2-2x_3 \leq 20 \\ x_1 + 2x_3 \leq 5 \\ x_1, \: x_2 \: x_3 \geq 0 $ What shall be the solution of the LLP after applying first iteration of the Simplex Method ... $x_1 = 0, x_2=0, \: x_3=10, \: Z=20$
Tiklu_95
answered
in
Numerical Methods
Jun 9, 2020
by
Tiklu_95
2.5k
views
ugcnetcse-june2019-paper2
simplex-method
1
vote
1
answer
7
UGC NET CSE | December 2018 | Part 2 | Question: 8
In PERT/CPM, the merge event represents _____ of two or more events. completion beginning splitting joining
Nbhardwaj
answered
in
Numerical Methods
May 14, 2020
by
Nbhardwaj
3.1k
views
ugcnetcse-dec2018-paper2
operation-research-pert-cpm
0
votes
1
answer
8
NIELIT 2017 OCT Scientific Assistant A (CS) - Section C: 7
The convergence of the bisection method is Cubic Quadratic Linear None
DIBAKAR MAJEE
answered
in
Numerical Methods
Apr 24, 2020
by
DIBAKAR MAJEE
986
views
nielit2017oct-assistanta-cs
non-gate
numerical-methods
1
vote
0
answers
9
NIELIT 2016 MAR Scientist C - Section B: 1
Choose the most appropriate option. The Newton-Raphson iteration $x_{n+1}=\dfrac{x_{n}}{2}+\dfrac{3}{2x_{n}}$ can be used to solve the equation $x^{2}=3$ $x^{3}=3$ $x^{2}=2$ $x^{3}=2$
Lakshman Bhaiya
asked
in
Numerical Methods
Apr 2, 2020
by
Lakshman Bhaiya
313
views
nielit2016mar-scientistc
non-gate
numerical-methods
0
votes
0
answers
10
NIELIT 2017 OCT Scientific Assistant A (IT) - Section B: 17
The convergence of the bisection method is Cubic Quadratic Linear None
closed
Lakshman Bhaiya
asked
in
Numerical Methods
Apr 1, 2020
by
Lakshman Bhaiya
192
views
nielit2017oct-assistanta-it
0
votes
2
answers
11
NIELIT 2017 DEC Scientist B - Section B: 3
Using bisection method, one root of $x^4-x-1$ lies between $1$ and $2$. After second iteration the root may lie in interval: $(1.25,1.5)$ $(1,1.25)$ $(1,1.5)$ None of the options.
Lakshman Bhaiya
asked
in
Numerical Methods
Mar 30, 2020
by
Lakshman Bhaiya
1.9k
views
nielit2017dec-scientistb
non-gate
numerical-methods
0
votes
1
answer
12
NIELIT 2017 DEC Scientist B - Section B: 20
Let $u$ and $v$ be two vectors in $R^2$ whose Eucledian norms satisfy $\mid u\mid=2\mid v \mid$. What is the value $\alpha$ such that $w=u+\alpha v$ bisects the angle between $u$ and $v$? $2$ $1$ $\dfrac{1}{2}$ $-2$
Lakshman Bhaiya
asked
in
Numerical Methods
Mar 30, 2020
by
Lakshman Bhaiya
376
views
nielit2017dec-scientistb
non-gate
vector-space
2
votes
1
answer
13
Is reading comprehension asked in IIITH
Does in iiith pgeee exam , does Reading comprehension is being asked. Do we need to prepare for it?
Winner
answered
in
Numerical Methods
Mar 29, 2019
by
Winner
490
views
iiith-pgee
4
votes
2
answers
14
ISRO2009-48
The cubic polynomial $y(x)$ which takes the following values: $y(0)=1, y(1)=0, y(2)=1$ and $y(3)=10$ is $x^3 +2x^2 +1$ $x^3 +3x^2 -1$ $x^3 +1$ $x^3 -2x^2 +1$
Devwritt
answered
in
Numerical Methods
Mar 10, 2019
by
Devwritt
1.7k
views
isro2009
polynomials
0
votes
3
answers
15
GATE CSE 1994 | Question: 3.4
Match the following items (i) Newton-Raphson (a) Integration (ii) Runge-Kutta (b) Root finding (iii) Gauss-Seidel (c) Ordinary Differential Equations (iv) Simpson's Rule (d) Solution of Systems of Linear Equations
Gurdeep Saini
answered
in
Numerical Methods
Dec 17, 2018
by
Gurdeep Saini
10.4k
views
gate1994
numerical-methods
easy
out-of-gate-syllabus
8
votes
1
answer
16
ISRO2009-44
A root $\alpha$ of equation $f(x)=0$ can be computed to any degree of accuracy if a 'good' initial approximation $x_0$ is chosen for which $f(x_0) > 0$ $f (x_0) f''(x_0) > 0$ $f(x_0) f'' (x_0) < 0$ $f''(x_0) >0$
Roman224
answered
in
Numerical Methods
Oct 7, 2018
by
Roman224
2.6k
views
isro2009
numerical-methods
1
vote
2
answers
17
Number Theory
A prison houses 100 inmates, one in each of 100 cells, guarded by a total of 100 warders. One evening, all the cells are locked and the keys left in the locks. As the first warder leaves, she turns every key, unlocking all the doors. The second warder ... every third key and so on. Finally the last warder turns the key in just the last cell. Which doors are left unlocked and why?
Subarna Das
answered
in
Numerical Methods
Apr 19, 2018
by
Subarna Das
519
views
number-theory
8
votes
3
answers
18
ISRO2017-3
Using Newton-Raphson method, a root correct to 3 decimal places of $x^3 - 3x -5 = 0$ 2.222 2.275 2.279 None of the above
stanchion
answered
in
Numerical Methods
Feb 27, 2018
by
stanchion
23.3k
views
isro2017
newton-raphson
non-gate
0
votes
0
answers
19
GATE CSE 1987 | Question: 11b
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.
closed
makhdoom ghaya
asked
in
Numerical Methods
Nov 15, 2016
by
makhdoom ghaya
576
views
gate1987
numerical-methods
simpsons-rule
out-of-gate-syllabus
0
votes
0
answers
20
GATE CSE 1987 | Question: 11a
Given $f(300)=2,4771; f(304) = 2.4829; f(305) = 2.4843$ and $f(307) = 2.4871$ find $f(301)$ using Lagrange's interpolation formula.
closed
makhdoom ghaya
asked
in
Numerical Methods
Nov 15, 2016
by
makhdoom ghaya
435
views
gate1987
numerical-methods
out-of-gate-syllabus
0
votes
0
answers
21
GATE CSE 1987 | Question: 1-xxv
Which of the following statements is true in respect of the convergence of the Newton-Rephson procedure? It converges always under all circumstances. It does not converge to a tool where the second differential coefficient changes sign. It does not converge to a root where the second differential coefficient vanishes. None of the above.
closed
makhdoom ghaya
asked
in
Numerical Methods
Nov 9, 2016
by
makhdoom ghaya
568
views
gate1987
numerical-methods
newton-raphson
out-of-gate-syllabus
3
votes
1
answer
22
UGC NET CSE | December 2014 | Part 3 | Question: 69
Five men are available to do five different jobs. From past records, the time (in hours) that each man takes to do each job is known and is given in the following table : Find out the minimum time required to complete all the jobs. $5$ $11$ $13$ $15$
Sanjay Sharma
answered
in
Numerical Methods
Aug 2, 2016
by
Sanjay Sharma
6.0k
views
ugcnetcse-dec2014-paper3
assignment-problem
hungarian-method
3
votes
2
answers
23
ISRO-2013-48
The Guass-Seidal iterative method can be used to solve which of the following sets? Linear algebraic equations Linear and non-linear algebraic equations Linear differential equations Linear and non-linear differential equations
kvkumar
answered
in
Numerical Methods
Jun 29, 2016
by
kvkumar
3.5k
views
isro2013
numerical-methods
guass-seidal-iterative-method
3
votes
2
answers
24
ISRO2009-51
The formula $P_k = y_0 + k \triangledown y_0+ \frac{k(k+1)}{2} \triangledown ^2 y_0 + \dots + \frac{k \dots (k+n-1)}{n!} \triangledown ^n y_0$ is Newton's backward formula Gauss forward formula Gauss backward formula Stirling's formula
naga praveen
answered
in
Numerical Methods
Jun 25, 2016
by
naga praveen
1.6k
views
isro2009
numerical-methods
4
votes
2
answers
25
ISRO2011-52
Given X: 0 10 16 Y: 6 16 28 The interpolated value X=4 using piecewise linear interpolation is 11 4 22 10
Kapil
answered
in
Numerical Methods
Jun 24, 2016
by
Kapil
2.8k
views
isro2011
interpolation
non-gate
3
votes
1
answer
26
ISRO2009-47
The formula $\int\limits_{x0}^{xa} y(n) dx \simeq h/2 (y_0 + 2y_1 + \dots +2y_{n-1} + y_n) - h/12 (\triangledown y_n - \triangle y_0)$ $- h/24 (\triangledown ^2 y_n + \triangle ^2 y_0) -19h/720 (\triangledown ^3 y_n - \triangle ^3 y_0) \dots $ is called Simpson rule Trapezoidal rule Romberg's rule Gregory's formula
ManojK
answered
in
Numerical Methods
Jun 15, 2016
by
ManojK
1.4k
views
isro2009
numerical-methods
non-gate
4
votes
1
answer
27
ISRO2009-46
The shift operator $E$ is defined as $E [f(x_i)] = f (x_i+h)$ and $E'[f(x_i)]=f (x_i -h)$ then $\triangle$ (forward difference) in terms of $E$ is $E-1$ $E$ $1-E^{-1}$ $1-E$
Kapil
answered
in
Numerical Methods
Jun 15, 2016
by
Kapil
7.9k
views
isro2009
5
votes
2
answers
28
GATE CSE 2000 | Question: 2.1
X, Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which of the following is true? k must be 1 k must be 0 k can take any value between 0 and 1 None of the above
confused_luck
answered
in
Numerical Methods
Jan 14, 2016
by
confused_luck
1.6k
views
gatecse-2000
numerical-methods
normal
30
votes
3
answers
29
GATE CSE 2006 | Question: 1, ISRO2009-57
Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i \neq 0$, $\forall i$. The minimum number of multiplications needed to evaluate $p$ on an input $x$ is: 3 4 6 9
srestha
answered
in
Numerical Methods
Nov 24, 2015
by
srestha
8.7k
views
gatecse-2006
numerical-methods
normal
isro2009
6
votes
2
answers
30
GATE CSE 1999 | Question: 1.23
The Newton-Raphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f’$ is the derivative of $f$. The method converges always only if $f$ is a polynomial only if $f(x_o) <0$ none of the above
Rajarshi Sarkar
answered
in
Numerical Methods
Jun 24, 2015
by
Rajarshi Sarkar
2.6k
views
gate1999
numerical-methods
newton-raphson
normal
out-of-syllabus-now
0
votes
1
answer
31
GATE CSE 1997 | Question: 4.10
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{b-a}{12} h^2 \max f’’(x), x \in [a, b]$ where $h$ is the width of the trapezoids. The minimum number of trapezoids guaranteed to ensure $E \leq 10^{-4}$ in computing $\ln 7$ using $f=\frac{1}{x}$ is 60 100 600 10000
Digvijay Pandey
answered
in
Numerical Methods
Jun 6, 2015
by
Digvijay Pandey
1.2k
views
gate1997
numerical-methods
trapezoidal-rule
normal
2
votes
2
answers
32
GATE CSE 1997 | Question: 1.2
The Newton-Raphson method is used to find the root of the equation $X^2-2=0$. If the iterations are started from -1, the iterations will converge to -1 converge to $\sqrt{2}$ converge to $\sqrt{-2}$ not converge
Rajarshi Sarkar
answered
in
Numerical Methods
Jun 5, 2015
by
Rajarshi Sarkar
10.6k
views
gate1997
numerical-methods
newton-raphson
normal
4
votes
2
answers
33
GATE CSE 1996 | Question: 2.5
Newton-Raphson iteration formula for finding $\sqrt[3]{c}$, where $c > 0$ is $x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 + c}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - c}{3x_n^2}$
Rajarshi Sarkar
answered
in
Numerical Methods
Jun 4, 2015
by
Rajarshi Sarkar
1.6k
views
gate1996
numerical-methods
newton-raphson
normal
out-of-syllabus-now
0
votes
3
answers
34
GATE CSE 1995 | Question: 2.15
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is $x_{k+1} = 3(x_k+b)/2x_k$ $x_{k+1} = (x_{k}^2+b)/2x_k$ $x_{k+1} = x_k-2x_k/\left(x^2_k+b\right)$ None of the above
Rajarshi Sarkar
answered
in
Numerical Methods
Jun 2, 2015
by
Rajarshi Sarkar
2.2k
views
gate1995
numerical-methods
newton-raphson
normal
out-of-gate-syllabus
1
vote
1
answer
35
GATE CSE 1993 | Question: 01.3
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree $1$ $2$ $3$ $4$
Rajarshi Sarkar
answered
in
Numerical Methods
Apr 26, 2015
by
Rajarshi Sarkar
4.6k
views
gate1993
numerical-methods
simpsons-rule
easy
out-of-gate-syllabus
multiple-selects
4
votes
1
answer
36
GATE IT 2007 | Question: 77
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2 - 2$, where $c > 0$. For which of the following values of $c$, does there exist a non-empty open interval $(a, b)$ such that the ... $0.25$ $0.35$ $0.45$ $0.5$ i only i and ii only i, ii and iii only i, ii, iii and iv
Rajarshi Sarkar
answered
in
Numerical Methods
Apr 13, 2015
by
Rajarshi Sarkar
1.2k
views
gateit-2007
numerical-methods
normal
non-gate
3
votes
1
answer
37
GATE IT 2004 | Question: 38
If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula? 8 8(1/3) 8(2/3) 9
Rajarshi Sarkar
answered
in
Numerical Methods
Apr 7, 2015
by
Rajarshi Sarkar
2.9k
views
gateit-2004
numerical-methods
lagranges-interpolation
normal
12
votes
3
answers
38
GATE CSE 2015 Set 3 | Question: 50
The velocity $v$ (in kilometer/minute) of a motorbike which starts form rest, is given at fixed intervals of time $t$ (in minutes) as follows: t 2 4 6 8 10 12 14 16 18 20 v 10 18 25 29 32 20 11 5 2 0 The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson's $1/3^{rd}$ rule is ________.
ashishacm
answered
in
Numerical Methods
Feb 20, 2015
by
ashishacm
5.9k
views
gatecse-2015-set3
numerical-methods
simpsons-rule
normal
numerical-answers
8
votes
2
answers
39
GATE CSE 2015 Set 2 | Question: 39
The secant method is used to find the root of an equation $f(x)=0$. It is started from two distinct estimates $x_a$ and $x_b$ for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if $f(x_b)$ is very small and then $x_b$ is ... $x_b - (x_b-x_a) f_b / (f_b-f(x_a)) $ $x_a - (x_b-x_a) f_a / (f_b-f(x_a)) $
Arjun
answered
in
Numerical Methods
Feb 20, 2015
by
Arjun
4.0k
views
gatecse-2015-set2
numerical-methods
secant-method
0
votes
1
answer
40
calculus
The estimate of $\int_{0.5}^{1.5}\frac{dx}{x}$ obtained using Simpson’s rule with threepoint function evaluation exceeds the exact value by (A) 0.235 (B) 0.068 (C) 0.024 (D) 0.012
Nisha kumari
asked
in
Numerical Methods
Jan 30, 2015
by
Nisha kumari
1.5k
views
numerical-methods
simpsons-rule
non-gate
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